I stumbled across this website just yesterday, and, having read a few posts, I'm really happy with the information and statistics provided. I'm feel like many of my questions have been answered. I do have a few questions more specific to my situation, however,and would be grateful for any help or advice that anyone might have.

I took my GRE last year and got decent scores on it. My math score was 74%, verbal was 67%, and my writing was 80%. I was really happy with that, and I felt that that would get me into some graduate math program.

I was going to begin studying for the math GRE last year, but was pretty busy, and it wasn't until now that I've really sat down with it. I don't feel particularly confident at the moment, and would like aa month or so to study and prepare myself before I take it. I hope to get at least 50%.

My dream school is UW Madison. I also want to try some other schools, and really reach in some situations. I do want to apply to UPenn (my favorite Ivy school at the moment), some other schools in the Wisconsin area (my home state and where all my family is), Pitt and some other Pittsburgh area schools (the city I currently live in).

I would like to get my Ph.D. My goal is to become a college math professor, write my own textbooks, and satiate my curiosity and love for math.

My questions are as follows:

1. I notice some people were putting research or publications down in their profile. I've not done anything like that, and a obviously, that would make an application more effective. Is there an opportunity for me to do research? I graduated 5 years ago and am a full time secondary ed teacher. Maybe a summer opportunity?

2. I went to a small private school for undergrad. It has no prestige, and frankly, it's known to be an easy school. I fear that this will hurt me (and my professors, who will write my letters of recommendation, won't be well-know either, so that won't help). Would you recommend that I seek a master's degree at a university first, before I try to apply to a bigger, more prestigious school?

3. Is there a link to the schools' rankings? I read through one from time magazine or something like that (I just googled it) but that didn't seem very official.

4. What advice would you have for me once I got accepted? How can I succeed at graduate level math?

5. Any advice for success on the Math GRE? I have the Princeton Review study book, and have been reading my way through it. I also have been working on problems on the practice exam provided from ETS. Anything else to help me out?

I have no "true" reason to apply to UPenn, per se, but I am attracted to the fact that it's in Pennsylvania, I really like what I read about their assistantship program (no teaching in the first year, which would help me acclimate), and it's an Ivy-league school. Am I Ivy material? I refuse to say "no," and as a result I'd like to "reach" for this school. If I get accepted (and get the assistantships) I'd be happy; if I never applied I'd be left wondering "What if?" and I just don't want that.

Of course, if I get a poor score on my subject GRE, I might forego applying there entirely (applications cost money, do they not?). I might even reconsider applying there if some others convince me that I'd be wasting my money, but again, I don't want to give up easily.

Anyway, thanks again for replying, I do appreciate your time and answers.

Do you have any professors that would really vouch for ability to do mathematical research?Without that and without any real research, you probably have little to no shot of making into a top 50 math phd program, even with a stellar math gre score.

I don't know if summer research is a viable option- There are REUs but these are for undergrads and very competitive. Your best bet is to do a masters first I would think. But keep in mind, these are still fairly competitive, but not on the same scale as a phd.

With regard to your gre scores- These actually don't matter for most schools. They usually don't look at your verbal or writing and some won't even look at you seriously if your quantitative percentile is less than 75.

Keep in mind that these programs are pretty small, and you'll be competing with some of the best students from top schools.

Sorry to be so negative. Let me know if you have more specific questions and I can do my best to help.

Last edited by blitzer6266 on Sun Sep 07, 2014 9:00 pm, edited 1 time in total.

After thinking for a while about the first problem you posted, I thought of using the washers method in the plane x=0

The outer radius squared is -z^2+2cz. The inner one is 2az, and you will integrate from 0 to 2(c-a)=A

So, pi int [0 to A] [-z^2 + 2(c-a)z] dz is in fact what the book says and you get to that in a couple of steps

I discovered, too, why the condition c<= 2a. The way I solved it, it doesn't really matter. But, if I would have decided to integrate along the y axis (as in using the shells metho) and c would have been ie 3a, the intersection of both curves would have been on the top right quarter of the circle instead of on the bottom right quarter.